The paper proposes a transparent and compact form of constitutive and equilibrium relations for the plane thermoelasticity of quasicrystal solids. The symmetry and positive definiteness of the ...obtained extended tensors of material constants are studied. An extension of the Stroh formalism is proposed for solving plane problems of thermoelasticity for quasicrystals. It is proved that the eigenvalues of the Stroh eigenvalue problem in the most general case of 3D quasicrystal materials do are purely complex. The relations between the matrices and vectors of phonon–phason elastic and thermoelastic coefficients of the proposed extended Stroh formalism are obtained. A fundamental solution to the plane problem of thermoelasticity of a quasicrystal medium is derived. The asymptotic behavior of physical and mechanical fields near the vertices of objects whose geometry can be modeled by a discontinuity line (cracks, thin inclusions) is studied, and the concepts of the corresponding generalized field (heat flux and phonon–phason stress) intensity factors are introduced. Examples of the influence of heat sources and sinks on an infinite quasicrystal medium containing a rectilinear heated crack are considered.
This article examines the main problems of modelling spherical (circular) particles. The main method of the initial process of filling lobules using the Cauchy and Reynolds problem is substantiated. ...An image of an object-oriented complex of free fall of a spherical particle and their many non-collision spheres is presented. Based on the obtained research results, the main parameters of the process of filling particles of heterogeneous materials. An example of visualization of the developed software product for filling material particles is given, taking into account a number of cross-sections of a cylindrical hopper in height. A histogram of the distribution of material particles from porosity over the volume of a cylindrical hopper is also constructed.
This scientific study deals with the main issues related to the process of filling inhomogeneous materials into a rectangular hopper. The article develops an algorithm for filling particles of ...structurally inhomogeneous materials. A micrograph of the structure of samples of inhomogeneous materials is presented. It was found that the structure of samples of heterogeneous materials consists of three layers: external, internal and impurities of various grinding aggregates. Based on microstructural analysis, the presence of particles of various shapes and sizes was justified. On the basis of which the main initial conditions for filling the package with spherical particles were described. The basic physical and mechanical properties of structurally inhomogeneous materials were studied using the obtained results. We also constructed an approximate dependence of porosity on the particle diameter of inhomogeneous materials.
In this scientific study, the main properties of structurally inhomogeneous materials are predicted by computer modelling methods. The automatic combination of a scanning microscope and a program ...cell makes it possible to view the procedure in detail before and after etching with the necessary increase in resolution. Based on the results obtained, we constructed a graphical dependence of the particle sizes of 40 XН steel on the iterative process, and also studied in detail the procedure for the effect of different particle sizes on porosity. We modelled 2D and 3D drawings of the PRT – 7 shaft part. We justified the predicted number of properties, in particular: porosity, particle shape, grain size, microstructure of the sample surface, pre-etching process, post-etching process, as well as the main advantages of the iterative process.
Granulometric characteristics of structurally inhomogeneous materials based on full-scale mounds of a powder mixture of different fractional composition are established. Regularities of backfilling ...of powder particles of different shapes and sizes are revealed, and changes in the polydispersity of powder particles within each fraction are justified. It is proved that with a decrease in the average particle size of structurally inhomogeneous AlCu2 materials in a single fraction, the size spread relative to this value of other particles increases. The results of calculating the porosity of backfills with particles of various shapes (round, triangular, and square) depending on the cross-sectional area of the lobules are presented. A three-dimensional diagram is constructed that shows the relationships between the fractional composition of powder particles, their average diameter, and the degree of inhomogeneity of homogeneous bronze AlCu2.
The paper presents a general boundary element approach for analysis of 3D cracks in anisotropic thermomagnetoelectroelastic solids. Dual boundary integral equations are derived, which kernels are ...explicitly written. These equations do not contain volume integrals in the absence of distributed body heat and extended body forces, which is advantageous comparing to the existing approaches. The issues on the boundary element solution of these equations are discussed in details. The efficient numerical evaluation of kernels based on the trapezoid rule is proposed. Modified Kutt's quadrature with Chebyshev nodes is derived for integration of singular and hypersingular integrals. Nonlinear polynomial mappings are adopted for smoothing the integrand at the crack front, which is advantageous for accurate evaluation of field intensity factors. Special shape functions are introduced, which account for a square-root singularity of extended stress and heat flux at the crack front. The issues on numerical determination of field intensity factors are discussed. Several numerical examples are presented, which show the efficiency (low computational time and high precision) of the proposed boundary element formulation.
•We consider a thermomagnetoelectroelastic Green’s function.•We apply Stroh formalism to reduce it to the improper integral.•We use residue calculus to evaluate this integral.
The paper presents ...studies on the Green’s function for thermomagnetoelectroelastic medium and its reduction to the contour integral. Based on the previous studies the thermomagnetoelectroelastic Green’s function is presented as a surface integral over a half-sphere. The latter is then reduced to the double integral, which inner integral is evaluated explicitly using the complex variable calculus and the Stroh formalism. Thus, the Green’s function is reduced to the contour integral. Since the latter is evaluated over the period of the integrand, the paper proposes to use trapezoid rule for its numerical evaluation with exponential convergence. Several numerical examples are presented, which shows efficiency of the proposed approach for evaluation of Green’s function in thermomagnetoelectroelastic anisotropic solids.
Root stem cell niche functioning requires the formation and maintenance of the specific “auxin-rich domain” governed by directional auxin transport and local auxin production. Auxin maximum ...co-localizes with the WOX5 expression domain in the quiescent center that separates mitotically active proximal and distal root meristems. Here we unravel the interconnected processes happening under WOX5 overexpression by combining
in vivo
experiments and mathematical modeling. We showed that WOX5-induced TAA1-mediated auxin biosynthesis is the cause, whereas auxin accumulation, PIN transporters relocation, and auxin redistribution between proximal and distal root meristems are its subsequent effects that influence the formation of the well-described phenotype with an enlarged root cap. These findings helped us to clarify the role of WOX5, which serves as a local QC-specific regulator that activates biosynthesis of non-cell-autonomous signal auxin to regulate the distal meristem functioning. The mathematical model with WOX5-mediated auxin biosynthesis and auxin-regulated cell growth, division, and detachment reproduces the columella cells dynamics in both wild type and under WOX5 dysregulation.
Summary
To date CYCB1;1 marker and cortex cell lengths have been conventionally used to determine the proliferation activity of the Arabidopsis root meristem. By creating a 3D map of mitosis ...distribution we showed that these markers overlooked that stele and endodermis save their potency to divide longer than the cortex and epidermis. Cessation of cell divisions is not a random process, so that mitotic activity within the endodermis and stele shows a diarch pattern. Mitotic activity of all root tissues peaked at the same distance from the quiescent center (QC); however, different tissues stopped dividing at different distances, with cells of the protophloem exiting the cell cycle first and the procambial cells being the last. The robust profile of mitotic activity in the root tip defines the longitudinal zonation in the meristem with the proliferation domain, where all cells are able to divide; and the transition domain, where the cell files cease to divide. 3D analysis of cytokinin deficient and cytokinin signaling mutants showed that their proliferation domain is similar to that of the wild type, but the transition domain is much longer. Our data suggest a strong inhibitory effect of cytokinin on anticlinal cell divisions in the stele.
Significance Statement
3D analysis of mitosis distribution in the Arabidopsis root meristem showed that there are two domains: in the proliferation domain all cells are able to divide; in the transition domain progressive cessation of cell divisions occurs within different cell files according to a diarch pattern. Protophloem ceases to divide the first, procambium the last, and the cortex cell starts to elongate in the middle.
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